It is also interesting to have a look to map (2.18) in [1]}. It is given by \(\mathsf {j} : \Lambda ^3 \mathrm {T}^*M \longrightarrow \mathrm {T} M \otimes \mathrm {T}^* M\)  with
\(\mathsf {j}(\gamma ) =\textstyle \sum _{i,j \in \mathbb {Z}_7}\star ((e_i \varphi ) \wedge (e_j \varphi ) \wedge \gamma ) \, e_i \otimes e_j^*.\) 
